In case anyone landed here on a search for replacing the factory stereo in a Toyota Corolla ZZE-122 (without climate control, manufactured late 2004), here are some things I learnt in getting the job done.
1. Disconnect the battery.
Take the -ve (black) wire off the battery, nothing to it. For safety, mainly.
2. Remove the old stereo.
I followed the steps on this thread (thanks Northy). To add to this, be very careful when removing the four 10mm hex-head screws that hold the stereo brackets in place - they can easily drop down into the chassis and are very hard to retrieve. I used a 10mm socket wrench to extract the screws with blu-tak in the end of the socket to hold onto the screws when they came out. Also, the two most deeply recessed screws are hard up against a perpendicular surface, meaning that you will probably need to use a socket that has a drive size of 1/4". Any socket with a drive size greater than 1/4" might be flared out at the drive connection, making it impossible to reach these screws.
3. Find out what sort of plugs your car has.
Mine had the double 'large pin' plugs, one 10-pin (of which only 7 are actually used), one 6-pin (of which only 4 are actually used).
4. Buy and rig an appropriate wiring harness for your car's plugs.
I bought the Aerpro APP0141 for $19 at Autobarn (I suppose the Aerpro 711761 would be a better choice, as it doesn't have ISO plugs, but I couldn't find it). I chopped off the ISO plugs from the APP0141, and stripped/soldered the wires onto the harness that was supplied as part of my head unit kit (the Pioneer 6150BT). The advantage here is that you don't chop up your car's wiring to fit your new stereo. This way, the harness connects the existing plugs in the car to the new head unit, and if you ever want to put the factory unit back in, simply remove the harness rigged specially for the new head unit.
A correct diagram for the wires in these plugs is here. Strip/solder/tape the connections from the Aerpro harness to the head unit harness. Note that I did not need either power antenna wires (H,I in the diagram) - because the ZZE-122 doesn't have a power aerial! ;)
5. Buy a 'pocket' with 'wings'/'ears' for single-DIN stereo installations.
The ZZE-122 and like cars have a double-DIN head unit space, but the space is a several mm wider than is 'standard'. To cover the gaps that will otherwise appear either side of the head unit (and below it), Aerpro also make an aftermarket pocket kit to suit this car, and others. I bought the Aerpro FP9016 pocket kit ($20 from a car audio shop) which comes with the pocket and wings to cover the gaps on the side. I've read online that fascia kits are the wrong way to go. I can at least vouch for this particular pocket kit - it worked fine for me.
6. Assemble the new head unit, pocket and wings to the car's stereo brackets.
This isn't hard to work out, as all these parts are modular and fit together as you might expect. Unfortunately, my stereo came with very shallow screws to connect the head unit to the car brackets. This was fine, but I couldn't use them to connect the 'wings' to the brackets, as the plastic holes were too deep. Fortunately, Bunnings sell 10g x 12mm screws with the same thread which I used successfully.
7. Plug the wiring harness into the car's stereo plugs and the new head unit.
Also plug the antenna in (mine fit right away; no need for an adapter).
8. Position the new head unit, brackets + pocket etc. into the slots
Screw everything in place again. I recommend using blu-tak in the sockets to keep hold of the screws - don't drop them into the interior!
9. Put all the interior back together.
I had to fiddle with the stereo bracket to fit the centre aircon vent fascia back around the stereo, because it has 'female'-type plastic sockets which clip onto the stereo bracket to hold everything in place. This thread (step 14) nearly got it right - I found that my ZZE-122 stereo bracket clips actually go into the centre aircon vent fascia sockets. Not getting these to slot in properly makes the dash prop up (wrong).
10. Re-connect the battery.
I found that after having the battery disconnected, my ZZE-122 master auto power window control (on the driver's side front door) no longer worked. This is a known problem - to fix this, simply manually drive each of the other windows all the way down, then all the way up, until the lights on the switches swap from flashing to solid - fixed.
